Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

SECTION 17.5 | Special Applications of the Chi-Square Tests 587
Now consider another instance, in which f e
= 10 and f o
= 14. The difference between the
observed and the expected frequencies is still 4, but the contribution of this cell to the total
chi-square value differs from that of the first case:
cell 5 s f o 2 f e d2
f e
5
s14 2 10d2
10
5 42
10 5 1.6
It should be clear that a small f e
value can have a great influence on the chi-square value.
This problem becomes serious when f e
values are less than 5. When f e
is very small, what
would otherwise be a minor discrepancy between f o
and f e
results in large chi-square
values. The test is too sensitive when f e
values are extremely small. One way to avoid
small expected frequencies is to use large samples.
LEARNING CHECK
ANSWERS
1. Effect size, as measured Cohen’s w, is determined by _______.
a. the proportions in the sample data
b. the proportions specified by the null hypothesis
c. the proportions in the sample data and the proportions specified by the null
hypothesis
d. neither the proportions in the sample data nor the proportions specified by the
null hypothesis
2. Under what circumstances is the phi-coefficient used instead of Cramér’s V to
measure effect size for the chi-square test for independence?
a. Only when the data form a 2 × 2 matrix.
b. Only when there are at least 3 rows or 3 columns in the data matrix.
c. Only when there are at least 3 rows and at least 3 columns in the data matrix.
d. Only when there are more than 3 rows and more than 3 columns in the data matrix.
3. Which of the following describes the assumptions and restrictions for a chi-square
test for independence?
a. Independent observations from a normal distribution.
b. Independent observations and no expected frequency smaller than 5.
c. Equal frequencies across each row of the data matrix.
d. The observations within each row are from a normal distribution.
1. C, 2. A, 3. B
17.5 Special Applications of the Chi-Square Tests
LEARNING OBJECTIVES
12. Explain the similarities and the differences between the chi-square test for
independence and the Pearson correlation.
13. Explain the similarities and the differences between the chi-square test for
independence and the independent-measures t test or ANOVA.
At the beginning of this chapter, we introduced the chi-square tests as examples of nonparametric
tests. Although nonparametric tests serve a function that is uniquely their own,
they also can be viewed as alternatives to the common parametric techniques that were